02/06/2020
The Human Resources Strategy for Researchers

PhD contract in the field of Computer science and Mathematics financed during 3 years by the University Clermont Auvergne

This job offer has expired


  • ORGANISATION/COMPANY
    Université Clermont Auvergne
  • RESEARCH FIELD
    Computer science
    Mathematics
  • RESEARCHER PROFILE
    First Stage Researcher (R1)
  • APPLICATION DEADLINE
    28/06/2020 00:00 - Europe/Brussels
  • LOCATION
    France › AUBIERE
  • TYPE OF CONTRACT
    Temporary
  • JOB STATUS
    Full-time
  • HOURS PER WEEK
    35 H
  • OFFER STARTING DATE
    01/10/2020
  • REFERENCE NUMBER
    UCA/ANR/014
  • IS THE JOB RELATED TO STAFF POSITION WITHIN A RESEARCH INFRASTRUCTURE?
    Yes

OFFER DESCRIPTION

Subject: Towards a mathematical understanding of neural networks through

mean-field analysis

Supervisor: Arnaud Guillin

Laboratory: Laboratoire Mathématiques Blaise Pascal

Email and phone: arnaud.guillin@uca.fr, 0473407090

Co-advisor(s): Manon Michel (LMBP)

Abstract (up to 10 lines):

If deep neural networks have proved their efficiency in a number of real

applications (game of Go, image analysis,…), we are far from understanding

the mathematical reasons behind this success. Recently a mean field analysis

has been introduced to get a new perspective on these algorithms. We will

pursue this direction and make links with statistical physics to hopefully gain a

profund understanding of these new statistical learning tools.

Skills: Mathematics, Probability, Statistics, Statistical learning, R,

Python

Keywords: Deep neural networks, statistical learning, mean field

analysis.

Description (up to 1 page):

The recent developments of Machine Learning algorithms have been marked

by popular successes, in particular coming from neural networks and their deep

implementation. However such successes are still poorly rigorously justified

and the rich behavior of deep neural nets is yet to be characterized by a wellunderstood

mathematical framework. In this thesis, we propose to work

towards such formalism by use of a mean field analysis. First developed for spin

systems and then applied in the 80s to shallow neural nets by physicists, the

mean field approach is the object of a recent renewed interest in mathematics

for such problems, thanks to its simplification power. However, this

simplification comes with limitations which need to be precisely analysed.

Eventually, the mean-field approach allows to draw natural bridges with

statistical physics, namely the spin-glass community, which will be also

investigated further.

References (recent):

"Mean field analysis of neural networks: A central limit theorem", Konstantinos Spiliopoulos,

Justin Sirignano, Stochastic Processes and their Applications , Volume 130, Issue 3, March

2020, pp. 1820-1852.

Deep Neural Networks Motivated by Partial Differential Equations, Lars Ruthotto, Eldad

Haber. Arxiv 2019.

"Mean field analysis of neural networks: a law of large numbers", Konstantinos Siliopoulos,

Justin Sirignano, 2019, SIAM Journal on Applied Mathematics, to appear.

Explorations on high dimensional landscapes, G. Ben Arous, L. Sagun, V. Ugur Guney, and

Yann Le Cun International Conference on learning representations, ICLR 2015

Références (up to ½ page):

How to candidate?

Contact the supervisor

More Information

Benefits

 

 
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Offer Requirements

  • REQUIRED EDUCATION LEVEL
    Other: Master Degree or equivalent

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Work location(s)
1 position(s) available at
Blaise Pascal Laboratory of Mathematics (LMBP)
France
Région Auvergne Rhône-Alpes
AUBIERE
63178
Campus Universitaire des Cézeaux TSA 60026 - CS 60026 3, Place Vasarely

Open, Transparent, Merit based Recruitment procedures of Researchers (OTM-R)

Know more about it at Université Clermont Auvergne

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EURAXESS offer ID: 528445

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